phase#
phase is a dictionary of arbitrarily labeled keys.
Each phase entry requires a key lattice that specifies the lattice structure in Pearson notation.
At least the type of the employed constitutive model for each active field (mechanical/elastic, mechanical/plastic, mechanical/eigen, thermal/source(s), or damage) is required; any further configuration details depend on the selected constitutive model.
It is recommended to construct phase entries based on the Reference Examples (also included in config.tar.xz) rather than from scratch.
Detailed documentation of the configuration keywords is available for these constitutive models:
mechanical
The basic layout is sketched in the following:
phase:
label_1:
lattice: lattice_1
mechanical:
elastic:
type: tbd
...:
plastic:
type: tbd
...:
eigen:
type: tbd
...:
damage:
type: tbd
...:
thermal:
source:
- type: tbd
...:
- type: tbd
...:
label_2:
lattice: lattice_2
mechanical:
elastic:
type: tbd
...:
plastic:
type: tbd
...:
eigen:
type: tbd
...:
damage:
type: tbd
...:
thermal:
source
- type: tbd
...:
- type: tbd
...:
label_N:
...
Reference Examples#
AISI304#
references:
- H.M. Ledbetter,
physica status solidi (a) 85(1):89-96, 1984,
https://doi.org/10.1002/pssa.2210850111
lattice: cF
rho: 7937.0
Ag#
references:
- https://en.wikipedia.org/wiki/Silver
lattice: cF
rho: 10490.0
Al#
references:
- https://en.wikipedia.org/wiki/Aluminium
lattice: cF
rho: 2700.0
Au#
references:
- https://en.wikipedia.org/wiki/Gold
lattice: cF
rho: 19300.0
Cu#
references:
- https://en.wikipedia.org/wiki/Copper
lattice: cF
rho: 8960.0
Fe#
references:
- https://en.wikipedia.org/wiki/Iron
lattice: cI
rho: 7874.0
Mg#
references:
- D. Tromans,
International Journal of Recent Research and Applied Studies 6(4):462-483, 2011,
https://www.arpapress.com/Volumes/Vol6Issue4/IJRRAS_6_4_14.pdf
lattice: hP
c/a: 1.62350
rho: 1740.0
Ni#
references:
- https://en.wikipedia.org/wiki/Nickel
lattice: cF
rho: 8908.0
Pt#
references:
- https://en.wikipedia.org/wiki/Platinum
lattice: cF
rho: 21450.0
Sn-beta#
references:
- J.A. Rayne and B.S. Chandrasekhar,
Physical Review 120(5):1658-1663, 1960,
https://doi.org/10.1103/PhysRev.120.1658
- https://en.wikipedia.org/wiki/Tin
lattice: tI
c/a: 0.5458 # T=300K (c=31.83nm, a=5.832nm)
rho: 7265.0
Ti#
references:
- https://www.totalmateria.com/page.aspx?ID=CheckArticle&site=ktn&NM=221
- https://en.wikipedia.org/wiki/Titanium
lattice: hP
c/a: 1.587
rho: 4506.0
W#
references:
- https://en.wikipedia.org/wiki/Tungsten
lattice: cI
rho: 19300.0
bcc#
lattice: cI
bct#
lattice: tI
c/a: 0.55
fcc#
lattice: cF
hcp#
lattice: hP
c/a: 1.6333
damage#
anisobrittle_cubic#
type: anisobrittle
output: [f_phi]
N_cl: [3]
g_crit: [0.5e+7]
s_crit: [0.006666]
dot_o_0: 1.e-3
p: 20
l_c: 1.0
mu: 0.001
isobrittle_generic#
type: isobrittle
output: [f_phi]
G_crit: 1400000.0
l_c: 1.0
mu: 0.001
mechanical#
eigen#
thermalexpansion_AISI304#
type: thermalexpansion
references:
- R.H. Bogaard et al.,
Thermochimica Acta 218:373-393, 1993,
https://doi.org/10.1016/0040-6031(93)80437-F,
fit to Fig. 6 (T_min=100K, T_max=1200K)
Alpha_11: 14.9e-6
Alpha_11,T: 1.838e-08
Alpha_11,T^2: -2.028e-11
Alpha_11,T^3: 9.173e-15
T_ref: 293.15
thermalexpansion_Al#
type: thermalexpansion
references:
- https://en.wikipedia.org/wiki/Thermal_expansion,
293.15K
Alpha_11: 23.1e-6
thermalexpansion_Au#
type: thermalexpansion
references:
- https://en.wikipedia.org/wiki/Thermal_expansion,
293.15K
Alpha_11: 14.e-6
thermalexpansion_C35E#
type: thermalexpansion
references:
- https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
fit to image description (Scilab code)
Alpha_11: 10.2e-6
Alpha_11,T: 1.260e-08
Alpha_11,T^2: -1.000e-11
T_ref: 293.15
thermalexpansion_Cu#
type: thermalexpansion
references:
- https://en.wikipedia.org/wiki/Thermal_expansion,
293.15K
Alpha_11: 17.e-6
thermalexpansion_Fe#
type: thermalexpansion
references:
- https://en.wikipedia.org/wiki/Thermal_expansion,
293.15K
Alpha_11: 11.8e-6
thermalexpansion_SiC-alpha#
type: thermalexpansion
references:
- Z. Li and R.C. Bradt,
Journal of the American Ceramic Society 69(12):863-866, 1986,
https://doi.org/10.1111/j.1151-2916.1986.tb07385.x
Alpha_11: 3.27e-6
Alpha_11,T: 3.25e-9
Alpha_11,T^2: -1.36e-12
Alpha_33: 3.18e-6
Alpha_33,T: 2.48e-9
Alpha_33,T^2: -8.51e-13
T_ref: 273.15
thermalexpansion_SiC-beta#
type: thermalexpansion
references:
- Z. Li and R.C. Bradt,
Journal of Materials Science 21:4366-4368, 1986,
https://doi.org/10.1007/BF01106557
Alpha_11: 3.19e-6
Alpha_11,T: 3.60e-9
Alpha_11,T^2: -1.68e-12
T_ref: 273.15
thermalexpansion_Sn-beta#
type: thermalexpansion
references:
- V.T. Deshpande and D.B. Sirdeshmukh,
Acta Crystallographica 15:294-295, 1962,
https://doi.org/10.1107/S0365110X62000742,
fit to Tab. 2 (T_min=30ºC, T_max=210ºC)
Alpha_11: 16.4e-6
Alpha_11,T: 1.799e-08
Alpha_11,T^2: 1.734e-10
Alpha_33: 32.6e-6
Alpha_33,T: 1.387e-08
Alpha_33,T^2: 5.794e-10
T_ref: 293.15
thermalexpansion_W#
type: thermalexpansion
references:
- https://en.wikipedia.org/wiki/Thermal_expansion,
293.15K
Alpha_11: 4.5e-6
thermalexpansion_X20Cr13#
type: thermalexpansion
references:
- https://commons.wikimedia.org/wiki/File:Coefficient_dilatation_lineique_aciers.svg,
fit to Scilab code for generating the image (T_min=100ºC, T_max=400ºC)
Alpha_11: 10.1e-6
Alpha_11,T: 5.000e-09
T_ref: 293.15
elastic#
Hooke_AISI304#
type: Hooke
references:
- H.M. Ledbetter,
physica status solidi (a) 85(1):89-96, 1984,
https://doi.org/10.1002/pssa.2210850111
C_11: 204.6e+9
C_12: 137.7e+9
C_44: 126.2e+9
Hooke_Ag#
type: Hooke
references:
- J.R. Neighbours and G.A. Alers,
Physical Review 111:707-712, 1958,
https://doi.org/10.1103/PhysRev.111.707,
fit to Tab. I (T_min=100K, T_max=300K)
- Y.A. Chang and L. Himmel,
Journal of Applied Physics 37:3567-3572, 1966,
https://doi.org/10.1063/1.1708903,
fit to Tab. II (T_min=300K, T_max=800K)
C_11: 124.1e+9
C_11,T: -3.148e+7
C_11,T^2: -6.594e+3
C_12: 93.7e+9
C_12,T: -1.657e+7
C_12,T^2: -4.220e+3
C_44: 46.4e+9
C_44,T: -1.775e+7
C_44,T^2: -1.973e+3
T_ref: 293.15
Hooke_Al#
type: Hooke
references:
- G.N. Kamm and G.A. Alers,
Journal of Applied Physics 35:327-330, 1964,
https://doi.org/10.1063/1.1713309,
fit to Tab. I (T_min=100K, T_max=300K)
- D. Gerlich and E.S. Fisher,
Journal of Physics and Chemistry of Solids 30:1197-1205, 1969,
https://doi.org/10.1016/0022-3697(69)90377-1,
fit to Tab. 2 (T_min=293K, T_max=900K)
C_11: 106.9e+9
C_11,T: -3.691e+7
C_11,T^2: -9.790e+3
C_12: 60.5e+9
C_12,T: -8.412e+6
C_12,T^2: -3.972e+3
C_44: 28.4e+9
C_44,T: -1.413e+7
C_44,T^2: -3.408e+3
T_ref: 293.15
Hooke_Au#
type: Hooke
references:
- J.R. Neighbours and G.A. Alers,
Physical Review 111:707-712, 1958,
https://doi.org/10.1103/PhysRev.111.707,
fit to Tab. II (T_min=100K, T_max=300K)
- Y.A. Chang and L. Himmel,
Journal of Applied Physics 37:3567-3572, 1966,
https://doi.org/10.1063/1.1708903,
fit to Tab. III (T_min=300K, T_max=800K)
C_11: 192.7e+9
C_11,T: -3.472e+7
C_11,T^2: 1.102e+3
C_12: 163.2e+9
C_12,T: -2.607e+7
C_12,T^2: 2.397e+3
C_44: 42.2e+9
C_44,T: -1.172e+7
C_44,T^2: -3.078e+3
T_ref: 293.15
Hooke_Cu#
type: Hooke
references:
- W.C. Overton Jr. and J. Gaffney,
Physical Review 98(4):969-977, 1955,
https://doi.org/10.1103/PhysRev.98.969,
fit to Tab. I (T_min=100K, T_max=300K)
- Y.A. Chang and L. Himmel,
Journal of Applied Physics 37:3567-3572, 1966,
https://doi.org/10.1063/1.1708903,
fit to Tab. II (T_min=300K, T_max=800K)
C_11: 168.9e+9
C_11,T: -3.332e+7
C_11,T^2: -1.074e+4
C_12: 121.8e+9
C_12,T: -1.402e+7
C_12,T^2: -9.003e+3
C_44: 75.8e+9
C_44,T: -2.555e+7
C_44,T^2: -2.188e+3
T_ref: 293.15
Hooke_Fe#
type: Hooke
references:
- D.J. Dever,
Journal of Applied Physics 43(8):3293-3301, 1972,
https://doi.org/10.1063/1.1661710,
fit to Tab. II (T_min=25ºC, T_max=880ºC)
C_11: 232.2e+9
C_11,T: -4.683e+7
C_11,T^2: -5.988e+4
C_12: 136.4e+9
C_12,T: -1.970e+7
C_12,T^2: 3.760e+3
C_44: 117.0e+9
C_44,T: -2.015e+7
C_44,T^2: -7.485e+2
T_ref: 293.15
Hooke_IN625#
type: Hooke
references:
- Z. Wang et al.,
Materials Science and Engineering:A 674:406-412, 2016,
https://doi.org/10.1016/j.msea.2016.08.010,
fit to Tab. 2 (last 3 rows)
C_11: 243.9e+9
C_11,T: -5.410e+7
C_12: 157.0e+9
C_12,T: -9.352e+6
C_44: 117.9e+9
C_44,T: -2.798e+7
T_ref: 293.15
Hooke_Mg#
type: Hooke
references:
- L.J. Slutsky and C.W. Garland,
Physical Review 107(4):972-976, 1957,
https://doi.org/10.1103/PhysRev.107.972,
fit to Tab. I (T_min=100K, T_max=300K)
C_11: 59.5e+9
C_11,T: -1.930e+7
C_11,T^2: -1.215e+4
C_12: 25.6e+9
C_12,T: -2.216e+6
C_12,T^2: -4.138e+3
C_44: 16.5e+9
C_44,T: -1.006e+7
C_44,T^2: -7.692e+3
C_33: 61.7e+9
C_33,T: -2.175e+7
C_33,T^2: -5.624e+3
C_13: 21.5e+9
C_13,T: -1.921e+6
C_13,T^2: -4.283e+3
T_ref: 293.15
Hooke_Ni#
type: Hooke
references:
- G.A. Alers,
Journal of Physics and Chemistry of Solids 13(1-2):40-55, 1960,
https://doi.org/10.1016/0022-3697(60)90125-6,
fit to Tab. 2 (T_min=100K, T_max=700K)
C_11: 251.0e+9
C_11,T: -4.967e+7
C_11,T^2: -3.327e+4
C_12: 150.0e+9
C_12,T: -3.714e+6
C_12,T^2: -7.414e+3
C_44: 123.7e+9
C_44,T: -3.621e+7
C_44,T^2: -8.017e+3
T_ref: 293.15
Hooke_Pt#
type: Hooke
references:
- S.M. Collard and R.B. McLellan,
Acta Metallurgica et Materialia 40:699-702, 1992,
https://doi.org/10.1016/0956-7151(92)90011-3
C_11: 373.42e+9
C_11,T: -8.929e+7
C_11,T^2: -1.298e+5
C_11,T^3: 1.2807e+2
C_11,T^4: -4.6114e-2
C_12: 241.74e+9
C_12,T: 5.705e+7
C_12,T^2: 0.4511e+5
C_12,T^3: -0.4860e+2
C_12,T^4: 1.446e-2
C_44: 77.65e+9
C_44,T: -1.342e+7
C_44,T^2: -0.1493e+5
C_44,T^3: 0.1260e+2
C_44,T^4: -0.6470e-2
T_ref: 0
Hooke_SAE1050-martensite#
type: Hooke
references:
- S.A. Kim and W.L. Johnson,
Materials Science & Engineering A 452-453:633-639, 2007,
https://doi.org/10.1016/j.msea.2006.11.147,
Tab. 1 (averaged for bcc)
C_11: 267.9e+9
C_12: 110.8e+9
C_44: 78.9e+9
Hooke_Sn-beta#
type: Hooke
references:
- J.A. Rayne and B.S. Chandrasekhar,
Physical Review 120(5):1658-1663, 1960,
https://doi.org/10.1103/PhysRev.120.1658,
fit to Tab. IV (T_min=77K, T_max=300K)
C_11: 72.6e+9
C_11,T: -4.135e+7
C_12: 59.4e+9
C_12,T: 6.726e+6
C_44: 22.2e+9
C_44,T: -1.870e+7
C_33: 88.8e+9
C_33,T: -5.381e+7
C_13: 35.8e+9
C_13,T: -2.870e+6
C_66: 24.1e+9
C_66,T: -1.709e+7
T_ref: 293.15
Hooke_TWIP-steel#
type: Hooke
references:
- D. Music et al.,
Applied Physics Letters 99(19):191904, 2007,
https://doi.org/10.1063/1.2807677
- S.L. Wong et al.,
Acta Materialia 118:140-151, 2016,
https://doi.org/10.1016/j.actamat.2016.07.032
C_11: 175.0e+9
C_12: 115.0e+9
C_44: 135.0e+9
Hooke_Ta#
type: Hooke
references:
- F.H. Featherston and J.R. Neighbours,
Physical Review 130(4):1324-1333, 1963,
https://doi.org/10.1103/PhysRev.130.1324,
fit to Tab. II (T_min=100K, T_max=300K)
C_11: 523.6e+9
C_11,T: -7.704e+7
C_11,T^2: -1.562e+5
C_12: 204.6e+9
C_12,T: -2.485e+7
C_12,T^2: -1.182e+5
C_44: 160.7e+9
C_44,T: -1.028e+7
C_44,T^2: 1.291e+4
T_ref: 293.15
Hooke_Ti#
type: Hooke
references:
- E.S. Fisher and C.J. Renken,
Physical Review 135(2A):A482-A494, 1964,
https://doi.org/10.1103/PhysRev.135.A482,
fit to Tab. IV (T_min=77K, T_max=923K)
C_11: 162.5e+9
C_11,T: -5.915e+7
C_11,T^2: 1.156e+4
C_12: 91.8e+9
C_12,T: 2.192e+7
C_12,T^2: -1.621e+4
C_44: 46.8e+9
C_44,T: -1.857e+7
C_44,T^2: -3.745e+3
C_33: 180.6e+9
C_33,T: -4.110e+7
C_33,T^2: 7.330e+3
C_13: 68.9e+9
C_13,T: 2.965e+6
C_13,T^2: -5.767e+3
T_ref: 293.15
Hooke_W-10at.%Re#
type: Hooke
references:
- R.A. Ayres et al.,
Journal of Applied Physics 46:1526-1530, 1975,
https://doi.org/10.1063/1.321804,
fit to Table IV (T_min=100K, T_max=300K)
C_11: 524.6e+9
C_11,T: -5.783e+07
C_11,T^2: -1.355e+05
C_12: 219.0e+9
C_12,T: 1.940e+07
C_12,T^2: 7.634e+04
C_44: 168.7e+9
C_44,T: -2.048e+07
C_44,T^2: -5.478e+04
T_ref: 293.15
Hooke_W-3at.%Re#
type: Hooke
references:
- R.A. Ayres et al.,
Journal of Applied Physics 46:1526-1530, 1975,
https://doi.org/10.1063/1.321804,
fit to Table IV (T_min=100K, T_max=300K)
C_11: 535.1e+9
C_11,T: -6.459e+07
C_11,T^2: -1.664e+05
C_12: 216.1e+9
C_12,T: 2.357e+07
C_12,T^2: 5.186e+04
C_44: 161.1e+9
C_44,T: -1.498e+07
C_44,T^2: -3.234e+04
T_ref: 293.15
Hooke_W#
type: Hooke
references:
- F.H. Featherston and J.R. Neighbours,
Physical Review 130(4):1324-1333, 1963,
https://doi.org/10.1103/PhysRev.130.1324,
fit to Tab. III (T_min=100K, T_max=300K)
C_11: 524.3e+9
C_11,T: -4.794e+07
C_12: 205.1e+9
C_12,T: -2.836e+06
C_44: 160.7e+9
C_44,T: -1.269e+07
T_ref: 293.15
Hooke_vanishing-Poisson-ratio#
type: Hooke
references:
- T. Maiti and P. Eisenlohr,
Scripta Materialia 145:37-40, 2018,
https://doi.org/10.1016/j.scriptamat.2017.09.047
C_11: 1.e+8
C_12: 1.e+6
C_44: 4.95e+7
plastic#
dislotungsten_W#
type: dislotungsten
references:
- D. Cereceda et al.,
International Journal of Plasticity 78:242-265, 2016,
https://doi.org/10.1016/j.ijplas.2015.09.002
- R. Gröger et al.,
Acta Materialia 56(19):5412-5425, 2008,
https://doi.org/10.1016/j.actamat.2008.07.037
output: [Lambda_sl]
N_sl: [12]
b_sl: [2.72e-10]
rho_mob_0: [1.0e+9] # estimated from section 3.2
rho_dip_0: [1.0] # not given
Q_s: [2.61154e-19] # 1.63 eV, Delta_H0
B: [8.3e-5]
omega: [9.1e+11] # nu_0
p_sl: [0.86]
q_sl: [1.69]
tau_Peierls: [2.03e+9]
h: [2.566e-10]
h_sl-sl: [0.009, 0.72, 0.009, 0.05, 0.05, 0.06, 0.09]
w: [2.992e-09] # 11b
# values in Cereceda et al. are high, using parameters from Gröger et al.
a_nonSchmid_110: [0.0, 0.56, 0.75] # Tab. 2
# (almost) no annhilation, adjustment needed for simulations beyond the yield point
i_sl: [1] # c, eq. (25)
D: 1.0e+20 # d_g, eq. (25)
D_a: 1.0 # d_edge = D_a*b
# disable climb (not discussed in Cereceda et al.)
D_0: 0.0
f_at: 1
Q_cl: 1.0
dislotwin_IF-steel#
type: dislotwin
references:
- K. Sedighiani et al.,
International Journal of Plasticity 134:102779, 2020,
https://doi.org/10.1016/j.ijplas.2020.102779
- K. Sedighiani et al.,
Mechanics of Materials, 164:104117, 2022,
https://doi.org/10.1016/j.mechmat.2021.104117
output: [rho_dip, rho_mob]
N_sl: [12, 12]
f_edge: [1.0, 1.0]
b_sl: [2.49e-10, 2.49e-10]
rho_mob_0: [2.81e+12, 2.8e+12]
rho_dip_0: [1.0, 1.0] # not given
v_0: [1.4e+3, 1.4e+3]
Q_sl: [1.57e-19, 1.57e-19] # Delta_F
tau_0: [454.e+6, 454.e+6]
p_sl: [0.325, 0.325]
q_sl: [1.55, 1.55]
i_sl: [23.3, 23.3]
D_a: 7.4 # C_anni
B: [0.001, 0.001]
h_sl-sl: [0.1, 0.72, 0.1, 0.053, 0.053, 0.073, 0.137, 0.72, 0.72, 0.053, 0.053, 0.053, 0.053, 0.073, 0.073, 0.073, 0.073, 0.073, 0.073, 0.137, 0.073, 0.073, 0.137, 0.073]
Q_cl: 5.4e-19 # no recovery!
D: 40.e-6 # estimated
dislotwin_TWIP-TRIP#
type: dislotwin
references:
- S.L. Wong et al.,
Acta Materialia 118:140-151, 2016,
https://doi.org/10.1016/j.actamat.2016.07.032
- K. Sedighiani et al.,
Mechanics of Materials, 164:104117, 2022,
https://doi.org/10.1016/j.mechmat.2021.104117
- L. Kubin et al.,
Acta Materialia 56:6040-6049,
https://doi.org/10.1016/j.actamat.2008.08.012
output: [rho_mob, rho_dip, gamma_sl, Lambda_sl, tau_pass, f_tw, Lambda_tw, f_tr]
# Glide
N_sl: [12]
f_edge: [1.0]
b_sl: [2.56e-10] # a/sqrt(2)
Q_sl: [3.5e-19]
p_sl: [0.325]
q_sl: [1.55]
B: [0.001]
i_sl: [30.0]
v_0: [1.4e+3]
tau_0: [5.5e+8] # adjusted
D_a: 2.0
Q_cl: 3.0e-19
rho_mob_0: [5.0e+10]
rho_dip_0: [5.0e+10]
h_sl-sl: [0.122, 0.122, 0.625, 0.07, 0.137, 0.137, 0.122]
# Twin
N_tw: [12]
b_tw: [1.47e-10] # a_cF/sqrt(6)
L_tw: 1.91e-7 # 1300 *b_tw
i_tw: 10.0
t_tw: [5.0e-8]
p_tw: [7] # A, adjusted
h_tw-tw: [1.0, 1.0]
h_sl-tw: [1.0, 1.0, 1.0]
# Transformation
N_tr: [12]
b_tr: [1.47e-10] # a_cF/sqrt(6)
L_tr: 2.21e-7 # 1500 *b_tr
i_tr: 10.0 # adjusted
t_tr: [1.0e-7]
p_tr: [4] # B, adjusted
V_mol: 7.09e-6
c/a_hP: 1.633
Delta_G: 1.2055e+2
Delta_G,T: 2.5515
Delta_G,T^2: 1.4952e-3
h_tr-tr: [1.0, 1.0]
h_sl-tr: [1.5, 1.5, 1.5]
# Twin & Transformation
T_ref: 293.15
Gamma_sf: 2.833e-2
Gamma_sf,T: 1.214e-4
Gamma_sf,T^2: 1.473e-7
x_c: 1.0e-9
V_cs: 1.67e-29
# Slip & Twin & Transformation
D: 5.0e-5
dislotwin_alpha-Brass-shearbanding#
type: dislotwin
references:
- N. Jia et al.,
Acta Materialia 60(3):1099-1115, 2012,
https://doi.org/10.1016/j.actamat.2011.10.047
- N. Jia et al.,
Acta Materialia 60:3415-3434, 2012,
https://doi.org/10.1016/j.actamat.2012.03.005
gamma_0_sb: 0.0001
tau_sb: 180.0e6 # tau_hat_sb
Q_sb: 4.0e-19 # Q_0
p_sb: 1.15
q_sb: 1.0
isotropic_free-surface#
type: isotropic
references:
- T. Maiti and P. Eisenlohr,
Scripta Materialia 145:37-40, 2018,
https://doi.org/10.1016/j.scriptamat.2017.09.047
output: [xi]
dot_gamma_0: 0.001
n: 20.
xi_0: 0.3e+6
xi_inf: 0.6e+6
a: 2.
h_0: 1.e+6
M: 1.
h: 1.
dilatation: True
kinehardening_317L#
type: kinehardening
references:
- J.A. Wollmershauser et al.,
International Journal of Fatigue 36(1):181-193, 2012,
https://doi.org/10.1016/j.ijfatigue.2011.07.008
output: [xi, chi, chi_flip, gamma_flip, gamma, sgn(gamma)]
N_sl: [12]
xi_0: [0.070e+9] # τ_0,for
xi_inf: [0.015e+9] # τ_1,for
h_0_xi: [0.065e+9] # θ_0,for
h_inf_xi: [0.045e+9] # θ_1,for
chi_inf: [0.027e+9] # τ_1,bs
h_0_chi: [55e+9] # θ_0,bs
h_inf_chi: [1.3e+9] # θ_1,bs
n: [20] # not mentioned in the reference
dot_gamma_0: [1e-4] # not mentioned in the reference
h_sl-sl: [1, 1, 1, 1, 1, 1, 1]
nonlocal_Al#
type: nonlocal
references:
- C. Kords,
On the role of dislocation transport in the constitutive description of crystal plasticity,
RWTH Aachen 2013,
http://publications.rwth-aachen.de/record/229993/files/4862.pdf
output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]
N_sl: [12]
b_sl: [2.86e-10]
V_at: 0.017e-27 # Omega
d_ed: [1.6e-9]
d_sc: [10.e-9]
i_sl: [60] # k_2 (lambda_0 in Tab. 7.1)
f_ed_mult: 0.1 # k_1
rho_u_ed_neg_0: [1.25e9] # 6e10 / (12*4)
rho_u_ed_pos_0: [1.25e9] # 6e10 / (12*4)
rho_u_sc_neg_0: [1.25e9] # 6e10 / (12*4)
rho_u_sc_pos_0: [1.25e9] # 6e10 / (12*4)
rho_d_ed_0: [0]
rho_d_sc_0: [0]
D_0: 7.e-29
Q_cl: 0.0 # no temperature dependency
Q_sol: 2.00272e-19 # 1.25 eV
c_sol: 1.5e-6 # correct unit?
f_sol: 2.0 # d_obst in multiples of b
tau_Peierls_ed: [.1e6]
tau_Peierls_sc: [.1e6]
w: 10 # w_k in multiple of b
p_sl: 1
q_sl: 1
nu_a: 50.e+9
B: 1.e-2
f_ed: 1.0 # k_3
h_sl-sl: [0, 0, 0.625, 0.07, 0.137, 0.137, 0.122] # Tab. 3.4
chi_GB: 0.0 # full blocking at GB
chi_surface: 1.0 # no blocking at surface
f_F: 0.0 # no line tension correction
sigma_rho_u: 0 # no random distribution
short_range_stress_correction: false
rho_significant: 1.e6
nonlocal_Ni#
type: nonlocal
references:
- C. Kords,
On the role of dislocation transport in the constitutive description of crystal plasticity,
RWTH Aachen 2013,
http://publications.rwth-aachen.de/record/229993/files/4862.pdf
output: [rho_u_ed_pos, rho_b_ed_pos, rho_u_ed_neg, rho_b_ed_neg, rho_u_sc_pos, rho_b_sc_pos, rho_u_sc_neg, rho_b_sc_neg, rho_d_ed, rho_d_sc]
N_sl: [12]
b_sl: [2.48e-10]
V_at: 0.012e-27 # Omega
d_ed: [2.6e-9]
d_sc: [12.e-9]
i_sl: [45] # k_2
f_ed_mult: 0.1 # k_1
rho_u_ed_neg_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_ed_pos_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_sc_neg_0: [6.e+10] # 2.88e12 / (12*4)
rho_u_sc_pos_0: [6.e+10] # 2.88e12 / (12*4)
rho_d_ed_0: [0]
rho_d_sc_0: [0]
D_0: 3.e-53
Q_cl: 0.0 # no temperature dependency
Q_sol: 1.79444e-19 # 1.12 eV
c_sol: 5.e-7 # correct unit?
f_sol: 1. # d_obst
tau_Peierls_ed: [.1e6]
tau_Peierls_sc: [.1e6]
w: 10 # w_k
p_sl: 1
q_sl: 1
nu_a: 50.e+9
B: 1.e-3
f_ed: 0.01 # k_3
h_sl-sl: [0, 0, 0.625, 0.07, 0.137, 0.137, 0.122] # Tab. 3.4
chi_GB: 0.0 # full blocking at GB
chi_surface: 1.0 # no blocking at surface
f_F: 0.0 # no line tension correction
sigma_rho_u: 0 # no random distribution
short_range_stress_correction: false
rho_significant: 1.e6
phenopowerlaw_AA6022-T4#
type: phenopowerlaw
references:
- T.J. Barrett and M. Knezevic,
Computer Methods in Applied Mechanics and Engineering 354:245-270, 2019,
https://doi.org/10.1016/j.cma.2019.05.035,
fitted to data shown in Fig 1 and Fig. 2a
output: [xi_sl, gamma_sl]
N_sl: [12]
dot_gamma_0_sl: [0.001]
n_sl: [20]
a_sl: [3.7]
xi_0_sl: [76.e+6]
xi_inf_sl: [266.e+6]
h_0_sl-sl: [1.02e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_Al#
type: phenopowerlaw
references:
- W.F. Hosford et al.,
Acta Metallurgica 8(3):187-199, 1960,
https://doi.org/10.1016/0001-6160(60)90127-9,
fitted to Fig. 5 ([111] and [001])
output: [xi_sl, gamma_sl]
N_sl: [12]
dot_gamma_0_sl: [7.5e-5]
n_sl: [20]
a_sl: [5.4]
xi_0_sl: [2.69e+6]
xi_inf_sl: [67.5e+6]
h_0_sl-sl: [0.2815e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_Au#
type: phenopowerlaw
references:
- D. Ma et al.,
Acta Materialia 103:796-808, 2016,
https://doi.org/10.1016/j.actamat.2015.11.016
- I. Kovács and G.Vörös,
International Journal of Plasticity 12:35-43, 1996,
https://doi.org/10.1016/S0749-6419(95)00043-7
- U.F. Kocks,
Metallurgical and Materials Transactions B 1:1121–1143, 1970,
https://doi.org/10.1007/BF02900224
output: [xi_sl, gamma_sl]
N_sl: [12]
dot_gamma_0_sl: [0.001]
n_sl: [83.3]
a_sl: [1.0]
xi_0_sl: [26.25e+6]
xi_inf_sl: [53.0e+6]
h_0_sl-sl: [75.0e+6]
h_sl-sl: [1, 1, 1.4, 1.4, 1.4, 1.4, 1.4]
phenopowerlaw_Cu#
type: phenopowerlaw
references:
- T. Takeuchi,
Transactions of the Japan Institute of Metals 16(10):629-640, 1975,
https://doi.org/10.2320/matertrans1960.16.629,
fitted to Fig. 3b ([111] and [001])
output: [xi_sl, gamma_sl]
N_sl: [12]
dot_gamma_0_sl: [3.e-3]
n_sl: [20]
a_sl: [0.6]
xi_0_sl: [1.6e+6]
xi_inf_sl: [96.4e+6]
h_0_sl-sl: [0.35e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_DP-steel-ferrite#
type: phenopowerlaw
references:
- C.C. Tasan et al.,
Acta Materialia 81:386-400, 2014,
https://doi.org/10.1016/j.actamat.2014.07.071
- U.F. Kocks,
Metallurgical and Materials Transactions B 1:1121–1143, 1970,
https://doi.org/10.1007/BF02900224
output: [xi_sl, gamma_sl]
N_sl: [12, 12]
dot_gamma_0_sl: [0.001, 0.001]
n_sl: [20, 20]
a_sl: [2.25, 2.25]
xi_0_sl: [95.e+6, 96.e+6]
xi_inf_sl: [222.e+6, 412.e+6]
h_0_sl-sl: [1.0e+9, 1.0e+9]
h_sl-sl: [1, 1.4, 1, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4]
phenopowerlaw_Mg#
type: phenopowerlaw
references:
- F. Wang et al.,
Acta Materialia 80:77-93, 2014,
https://doi.org/10.1016/j.actamat.2014.07.048
output: [xi_sl, xi_tw]
N_sl: [3, 3, 6, 0, 6] # basal, prism, 1. pyr<a>, -, 2. pyr<c+a>
N_tw: [6, 0, 6] # tension, -, compression
xi_0_sl: [10.e+6, 55.e+6, 60.e+6, 0., 60.e+6]
xi_inf_sl: [40.e+6, 135.e+6, 150.e+6, 0., 150.e+6]
xi_0_tw: [40.e+6, 0., 60.e+6]
a_sl: [2.25, 2.25, 2.25, 1, 2.25]
dot_gamma_0_sl: [0.001, 0.001, 0.001, 0, 0.001]
dot_gamma_0_tw: [0.001, 0, 0.001]
n_sl: [20, 20, 20, 1, 20]
n_tw: [20, 1, 20]
f_sat_sl-tw: [10.0, 10.0, 10.0, 0, 10.0]
h_0_sl-sl: [0.5e+9, 0.5e+9, 0.5e+9, 0, 0.5e+9]
h_0_tw-tw: [50.0e+6, 0, 50.0e+6]
h_0_tw-sl: [0.15e+9, 0, 0.15e+9]
h_sl-sl: [+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, 1.0, 1.0, -1.0,
-1.0, -1.0, -1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0] # unused entries are indicated by -1.0
h_tw-tw: [+1.0, 1.0, -1.0, -1.0, -1.0, -1.0, 1.0, -1.0, 1.0, 1.0,
-1.0, 1.0] # unused entries are indicated by -1.0
h_tw-sl: [1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0,
1.0, -1.0, -1.0, -1.0, -1.0, -1.0, +1.0, -1.0, 1.0, -1.0] # unused entries are indicated by -1.0
h_sl-tw: [1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0, 1.0, -1.0,
1.0, -1.0, -1.0, -1.0, -1.0, -1.0, +1.0, -1.0, 1.0] # unused entries are indicated by -1.0
phenopowerlaw_Pt-5%Cu#
type: phenopowerlaw
references:
- K.M. Jackson and C. Lang,
Platinum Metals Review 50:15-19, 2006,
https://doi.org/10.1595/147106705X93359,
fitted to Fig. 5 (Pt-5% Cu recrystallised)
output: [xi_sl, gamma_sl]
N_sl: [12]
dot_gamma_0_sl: [0.001]
n_sl: [20]
a_sl: [0.9]
xi_0_sl: [0.114e+9]
xi_inf_sl: [0.207e+9]
h_0_sl-sl: [0.7812e+9]
h_sl-sl: [1, 1, 5.123, 0.574, 1.123, 1.123, 1]
phenopowerlaw_Sn-beta#
type: phenopowerlaw
references:
- A. Chakraborty and P. Eisenlohr,
Journal of Applied Physics 124:025302, 2018,
https://doi.org/10.1063/1.5029933
output: [xi_sl, gamma_sl]
N_sl: [2, 2, 2, 4, 2, 4, 2, 2, 4, 0, 0, 8]
n_sl: [6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 6.0, 1, 1, 6.0]
a_sl: [2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 2.0, 1.0, 1.0, 2.0]
h_0_sl-sl: [20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 20e+6, 0.0, 0.0, 20e+6]
xi_0_sl: [8.5e+6, 4.3e+6, 10.4e+6, 4.5e+6, 5.6e+6, 5.1e+6, 7.4e+6, 15.0e+6, 6.6e+6, 0.0, 0.0, 12.0e+6]
xi_inf_sl: [11.0e+6, 9.0e+6, 11.0e+6, 9.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 10.0e+6, 9.0e+6, 0.0, 0.0, 13.0e+6]
h_sl-sl: [+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, # 50
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, # 100
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0,
-1.0, -1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, -1.0, -1.0, 1.0, 1.0, -1.0, -1.0, 1.0, 1.0, 1.0, # 150
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0] # unused entries are indicated by -1.0
dot_gamma_0_sl: [2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 2.6e-8, 1.0, 1.0, 2.6e-8]
phenopowerlaw_Ti#
type: phenopowerlaw
references:
- C. Zambaldi et al.,
Journal of Materials Research 27(1):356-367, 2021,
https://doi.org/10.1557/jmr.2011.334
- L. Wang et al.,
Acta Materialia 132:598-610, 2017,
https://doi.org/10.1016/j.actamat.2017.05.015
output: [gamma_sl]
N_sl: [3, 3, 0, 12] # basal, prism, -, 1. pyr<c+a>
dot_gamma_0_sl: [0.001, 0.001, 0.0, 0.001]
n_sl: [20, 20, 1, 20]
a_sl: [2.0, 2.0, 1.0, 2.0]
# C. Zambaldi et al.:
xi_0_sl: [0.349e+9, 0.15e+9, 0.0, 1.107e+9]
xi_inf_sl: [0.568e+9, 1.50e+9, 0.0, 3.420e+9]
# L. Wang et al. :
# xi_0_sl: [127.e+6, 96.e+6, 0.0, 240.e+6]
h_0_sl-sl: [0.2e+9, 0.2e+9, 0.0, 0.2e+9]
h_sl-sl: [+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, -1.0, -1.0,
-1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0,
+1.0, 1.0, 1.0, 1.0, 1.0, 1.0] # unused entries are indicated by -1.0
phenopowerlaw_bcc_martensite#
# Tasan et.al. 2015 Acta Materalia
# Tasan et.al. 2015 International Journal of Plasticity
# Diehl et.al. 2015 Meccanica
type: phenopowerlaw
N_sl: [12, 12]
dot_gamma_0_sl: [0.001, 0.001]
n_sl: [20, 20]
a_sl: [2.0, 2.0]
xi_0_sl: [405.8e+6, 456.7e+6]
xi_inf_sl: [872.9e+6, 971.2e+6]
h_0_sl-sl: [563.0e+9, 563.0e+9]
h_sl-sl: [1, 1.4, 1, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4, 1.4]
thermal#
AISI304#
references:
- B.F. Blackwell et al.
Proceedings of 34th National Heat Transfer Conference 2000
https://www.osti.gov/servlets/purl/760791
- R.H. Bogaard et al.
Thermochimica Acta 218:373-393, 1993
https://doi.org/10.1016/0040-6031(93)80437-F
C_p: 470.0
K_11: 14.34
Al#
references:
- J.G. Hust and A.B. Lankford,
Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
US Department of Commerce, Boulder, Colorado, 1984,
fit to Tab. 3.4.1 (RRR=1000, T_min=200K, T_max=900K)
- https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
output: [T]
K_11: 2.374e+2
K_11,T: 8.952e-3
K_11,T^2: 2.650e-5
K_11,T^3: -5.687e-7
K_11,T^4: 6.407e-10
T_ref: 293.15
C_p: 910.0
Au#
references:
- https://de.wikipedia.org/wiki/Gold
C_p: 128.0
K_11: 320.0
Cu#
references:
- J.G. Hust and A.B. Lankford,
Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
US Department of Commerce, Boulder, Colorado, 1984,
fit to Tab. 2.4.1 (RRR=300, T_min=150K, T_max=1000K)
- https://www.mit.edu/~6.777/matprops/copper.htm
output: [T]
K_11: 4.005e+2
K_11,T: -1.075e-1
K_11,T^2: 3.293e-4
K_11,T^3: -7.533e-7
K_11,T^4: 5.223e-10
T_ref: 293.15
C_p: 385.0
Fe#
references:
- J.G. Hust and A.B. Lankford,
Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
US Department of Commerce, Boulder, Colorado, 1984,
fit to Tab. 4.4.1 (RRR=300, T_min=150K, T_max=1000K)
- https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
output: [T]
K_11: 8.034e+1
K_11,T: -1.216e-1
K_11,T^2: 1.327e-4
K_11,T^3: -7.993e-8
T_ref: 293.15
C_p: 450.0
Ni#
references:
- Y.S. Touloukian et al.,
TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
IFI/Plenum, 1970,
fit to Tab. 35R (T_min=80K, T_max=500K)
- https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
output: [T]
K_11: 9.311e+1
K_11,T: -8.719e-2
K_11,T^2: -3.793e-4
K_11,T^3: -4.003e-6
K_11,T^4: 2.676e-8
T_ref: 293.15
C_p: 440.0
Sn-beta#
references:
- Y.S. Touloukian et al.,
TPRC Data Series Volume 1. Thermal conductivity - metallic elements and alloys,
IFI/Plenum, 1970,
fit to Tab. 61R (T_min=80K, T_max=500K)
- https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
output: [T]
K_11: 7.495e+1
K_11,T: -5.646e-2
K_11,T^2: 1.420e-5
K_11,T^3: -5.390e-7
K_11,T^4: 4.012e-9
K_33: 5.204e+1
K_33,T: -3.940e-2
K_33,T^2: 7.037e-6
K_33,T^3: -3.738e-7
K_33,T^4: 2.873e-9
T_ref: 293.15
C_p: 210.0
W#
references:
- J.G. Hust and A.B. Lankford,
Thermal Conductivity of Aluminum, Copper, Iron, and Tungsten from 1K to the Melting Point,
US Department of Commerce, Boulder, Colorado, 1984,
fit to Tab. 5.4.1 (RRR=300, T_min=100K, T_max=2000K)
- https://www.mit.edu/~6.777/matprops/tungsten.htm
output: [T]
K_11: 1.750e+2
K_11,T: -1.809e-1
K_11,T^2: 2.257e-4
K_11,T^3: -1.395e-7
K_11,T^4: 3.192e-11
T_ref: 293.15
C_p: 132.51
adiabatic#
C_p: 1
K_11: 0
K_33: 0
fast-convection#
C_p: 1
K_11: 1.e+30
K_33: 1.e+30
steel-0.5C#
references:
- https://www.engineeringtoolbox.com/thermal-conductivity-metals-d_858.html
- https://www.engineeringtoolbox.com/specific-heat-metals-d_152.html
C_p: 490.0
K_11: 54.0
source#
dissipation_generic#
type: dissipation
kappa: .9
externalheat_ramp-and-hold#
type: externalheat
f: [1, 1, 0, 0]
t: [0, 500, 500.001, 1000]